Stationary Solutions of a Mathematical Model for Formation of Coral Patterns

Lekam Watte Somathilake; Janak R. Wedagedera

doi:10.4236/am.2015.66100

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AM> Vol.6 No.6, June 2015

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Stationary Solutions of a Mathematical Model for Formation of Coral Patterns

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DOI: 10.4236/am.2015.66100 2,262 Downloads 2,611 Views

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Lekam Watte Somathilake¹, Janak R. Wedagedera²

Affiliation(s)

¹Department of Mathematics, Faculty of Science, University of Ruhuna, Matara, Sri Lanka.
²Simcyp-CERTARA Limited, Blades Enterprise Centre, Sheffield, UK.

ABSTRACT

A reaction-diffusion type mathematical model for growth of corals in a tank is considered. In this paper, we study stationary problem of the model subject to the homogeneous Neumann boundary conditions. We derive some existence results of the non-constant solutions of the stationary problem based on Priori estimations and Topological Degree theory. The existence of non-constant stationary solutions implies the existence of spatially variant time invariant solutions for the model.

KEYWORDS

Reaction-Diffusion Equations, Stationary Solutions, Priori Estimates, Topological Degree Theory

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Somathilake, L. and Wedagedera, J. (2015) Stationary Solutions of a Mathematical Model for Formation of Coral Patterns. Applied Mathematics, 6, 1099-1106. doi: 10.4236/am.2015.66100.

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